In the traditional system identification means, quantification operations can be carried out. These operations are generally modeled by adding white noise b to a signal y that is quantified:yquantified=y+b 
This noise is all the weaker as the number of bits on which the quantification is done is higher. Thus, to identify a system using a traditional identification method, it is preferable to have an analog digital converter (ADC) with a high resolution.
In that case, with a small number of measurements, it is possible to be freed from the quantification noise.
In the case where an ADC with low precision is used, a significant number of measuring points may be necessary.
One very widespread traditional identification method is the so-called method “of least squares.” This method consists of making a parameterized model θidéal of the transfer function of the system and minimizing the square deviation between the measured values and estimated values output from the model Ĥθ, the system's input e also being known:θidéal=arg min(∥Ĥθ(e)−yquantifie∥2)
In the case where the quantification noise is low enough, the quantified signal yquantifié can be likened to the actual signal y. In that case, if the model Ĥθ is linear, the parameterized model θidéal can be expressed analytically. The input e of the system one wishes to identify is generally white noise.
The method of least squares has the drawback, in particular, of requiring that a high-resolution ADC be integrated.
In another method, called “KLV” (Kessler Landau Voda) (FIG. 1) (block referenced 2), the transfer function H of a system placed in a non-linear feedback loop is identified, including an adjustable hysteresis comparator 3. This comparator makes it possible to cause the system 2 to oscillate. Information can be deduced on the system through the appearance of said oscillations. A one-bit ADC 4 is provided in output of the system. It is then possible to connect, using analytical relationships, the amplitude and the frequency of the oscillations arising in the system to the frequency response value of the system. Each hysteresis value has a corresponding point on the frequency response curve.
Such a method has several drawbacks. First, the validity of the analytical relationships used is based on an approximation called approximation of the first harmonic of the comparator. Moreover, such a method requires a precise measurement of the amplitude and phase of the oscillations, the amplitude measurement requiring a high resolution ADC.
Another method, called “OBT” (Oscillation-Based Test), close to the KLV method, consists of inserting the system one wishes to identify and having a transfer function H, in a non-linear loop including a comparator 6. The return gain (block referenced 7) is adjusted to observe oscillations preferably having as sinusoidal a shape as possible. In this way, it is possible to deduce, using the first harmonic hypothesis, the parameters of the transfer function H using analytical relationships, as for the KLV method.
This method also has the drawback of requiring a precise measurement of the amplitude of the oscillations at the input of the comparator, i.e. a high-resolution ADC 5 (FIG. 2).
An identification method called the “LCM”(Limit Cycle Measurement) method makes it possible to precisely determine the natural frequency and damping of a second order system using two frequency measurements (FIGS. 3A and 3B).
A first measurement is done by placing the system to be identified with transfer function H in a loop including a comparator 9 and a differentiator 8 (FIG. 3A).
A second measurement is done by replacing, in said loop, the differentiator 8 with an integrator 10 (FIG. 3B).
It is thus possible to obtain a relationship between the frequency of the measured oscillations in output from the comparator 6 and the value of the natural frequency and damping of the system to be identified.
This method is based on two digital measurements, the frequency measurement being done by counting the number of switches of the comparator over a given duration. This method has several drawbacks.
It is only applicable to analog integrator or differentiator filters or on samples. Also, in the case of implementation using a digital circuit, it is necessary to have an Analog Digital Converter (ADC) with a good resolution to inject the output of the integrator into the system.
In the “CLCM” (Complex Limit Cycle Measurement) method, the system to be identified 12 is placed in a non-linear feedback loop including a sampled comparator 13 having a sampling period Ts, a digital programmable digital filter 14, and an ADC 15 (FIG. 4).
Depending on the value chosen for the coefficients of the digital filter, binary oscillations or “limit cycles” can be seen in output from the comparator 13. These limit cycles differ from those observed by implementing the KLV method or LCM method in that they have a period that is a multiple of the sampling period Ts. The switching moments of the comparator 13 correspond to sampling moments. Thus, measuring a limit cycle corresponding to a set of coefficients of the programmable filter 14 is completely digital.
This method in particular has the drawback of having to generate long limit cycles to implement it.
The KLV and LCM methods make it possible to establish, at the cost of an approximation, a relationship between the magnitudes measured and parameters one wishes to determine.
The KLV and OBT methods require a high-resolution ADC, while the LCM method requires an ADC with a good resolution. These methods yield insufficient results when the sampling frequency is high.
The CLCM method has a performance that is independent of the sampling frequency, at the cost of heavier processing than that done with the other methods. Moreover, with such a method, good precision requires that long limit cycles be generated, which can be problematic.
The use of the aforementioned closed loop identification methods is particularly problematic when the system to be identified is an electromechanical device in the form of a MEMS. The risk is of not being able to perform the identification at the right operating point, in as much as exciting a MEMS on one of its modes tends to very quickly amplify non-linear phenomena. To offset this, it is possible to add an amplitude gain control (AGC) to the identification system, which may require the use of a high-precision ADC.
The aforementioned identification methods have the drawback of requiring an analog-digital conversion with a significant resolution in output, which makes them more complex to implement and creates cost problems.
The problem arises of finding a new identification method that does not have the aforementioned drawbacks.